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  • Articles  (117)
  • Computational Chemistry and Molecular Modeling  (104)
  • Calcification  (13)
  • 1980-1984
  • 1965-1969  (117)
  • 1925-1929
  • 1969  (117)
  • 1928
  • 1926
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  • Articles  (117)
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  • 1980-1984
  • 1965-1969  (117)
  • 1925-1929
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Calcified tissue international 4 (1969), S. 260-268 
    ISSN: 1432-0827
    Keywords: Cartilage ; Histochemistry ; Staining ; Protein ; Polysaccharide ; Calcification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé Des coupes de cartilage épiphysaire frais de jeunes rats, effectuées à la main, sont colorées à pH=4,5 dans des solutions à 0,01% de divers colorants cationiques, appartenant aux groupes de la thiazine, oxazine, azine, triphénylméthane, acridine, et phthallocyanine. Les granules intracellulaires métachromatiques, mises en évidence antérieurement par le bleu de toluidine, sont également identifiées à l'aide de l'azur A, le bleu de méthylène et le bleu de crésyl. Les granules se colorent moins bien à la thionine, le rouge neutre, la safranine O, le bleu de toluylène et l'acridine orange. Dans les conditions utilisées, la matrice de la zone de réserve et la matrice de la zone hypertrophique inférieure (en voie de calcification) se colorent, alors que les matrices des zones prolifératives et hypertrophiques supérieures ne prennent pas les colorants. La gallocyanine, le violet cristal, la fuchsine basique, l'azocarmin B, le bleu de gallamine et la bleu alcian ne se colorent pas ou donnent des réactions colorées différentes de celles décrites ci-dessus. Il semble que le pK et le poids moléculaire des colorants jouent un rôle important, mais ils ne paraissent pas être les seuls facteurs intervenant dans la coloration des granules. Un changement, lié à la calcification, semble intervenir au niveau du matériel métachromatique (probablement des polysaccharides protéiques), aussi bien dans la matrice que les cellules cartilagineuses épiphysaires.
    Abstract: Zusammenfassung Handpräparierte Schnitte von frischem Epiphysenknorpel junger Ratten wurden bei einem pH von 4,5 in 0,01% igen Lösungen verschiedener kationischer Farbstoffe folgender Klassen gefärbt: Thiazin, Oxazin, Azin, Triphenylmethan, Acridin und Phthalocyanin. Die intracellulären β-und γ-metachromatischen Granula, erstmals mit Toluidinblau im frischen Gewebe nachgewiesen, konnten auch gut mit Azur A, Methylenblau und Brillantkresylblau dargestellt werden. Die Granula konnten ebenfalls, aber weniger gut, mit Thionin, Neutralrot, Safranin D, Toluylenblau und Acridinorange gefärbt werden. Unter diesen Färbungsbedingungen werden die inaktive Matrixzone und die untere hypertrophische (verkalkende) Matrixzone angefärbt, während die proliferative und die obere hypertrophische Matrixzone sich nicht färben. Gallocyanin, Kristallviolett, basisches Fuchsin, Azokarmin B, Gallaminblau und Alzianblau färbten entweder gar nicht, oder gaben ein anderes als das obenbeschriebene Färbemuster. Es wird vorgeschlagen, daß das pK und das Molekulargewicht der Farbstoffe wichtig aber nicht unbedingt die einzigen Faktoren sind, die die Färbung der Granula bestimmen. Die Resultate zeigen, daß eine Veränderung im metachromatischen Material (vermutlich Proteinpolysaccharide) vorliegt, und zwar sowohl in der Matrix als in den Zellen des Epiphysenknorpels; diese Veränderung scheint im Zusammenhang mit der Verkalkung zu stehen.
    Notes: Abstract Hand-cut sections of fresh epiphyseal cartilage from young rats were stained at pH 4.5 in 0.01% solutions of various cationic dyes of the thiazine, oxazine, azine, triphenylmethane, acridine, and phthallocyanin classes. The intracellular β-and γ-metachromatic granules, previously demonstrated in fresh tissues with toluidine blue, were also demonstrated well with azure A, methylene blue, and brilliant cresyl blue. The granules were also demonstrated, but not as well, by thionin, neutral red, safranin O, toluylene blue, and acridine orange. Under the conditions of staining, the reserve zone matrix and the lower hypertrophic (calcifying) zone matrix stained, whereas the proliferative and upper hypertrophic zone matrix did not stain. Gallocyanin, crystal violet, basic fuchsin, azocarmine B, gallamine blue, and alcian blue either did not stain, or gave a different pattern of staining from that described above. It is suggested that the pK and molecular weight of the dyes are important, but not necessarily the only factors in determining the staining of the granules. The results indicate that there is a change in the metachromatic material (presumably proteinpolysaccharide) in both the matrix and cells of epiphyseal cartilage, which appears to be related to calcification.
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  • 2
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    Springer
    Calcified tissue international 4 (1969), S. 20-38 
    ISSN: 1432-0827
    Keywords: Calcification ; Epiphyseal Cartilage ; Bone ; Electrolytes ; Organic matrices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé Un procédé de dissection a été mis au point pour permettre l'analyse zonale du cartilage de l'épiphyse des os de la jambe d'un foetus bovin. Des échantillons de tissu complet et lavé venant des différentes zones ont été analysés pour déterminer leur contenu en électrolyte et en constituants organiques, ainsi que pour leur densité, cendres et humidité. Les résultats ont montré que lorsque la quantité de cendres et la densité augmentaient, l'eau contenu dans le tissu diminuait. Les quantités de cendres dans les zones de cartilage en voie de calcification étaient plus grandes qu'il avait été. Quand elles étaient exprimées comme un pourcentage du poids sec, elles étaient les plus importantes dans le cartilage lavé calcifié que dans le autre zones. Au début de la minéralisation du cartilage, la quantité de Na (m moles/l de tissu frais) diminuait tandis que celles du Ca et du P inorganique augmentaient. Les niveaux de Mg augmentaient pendant que la calcification se poursuivait, mais seulement à une faction du taux du Ca et du P. Les rapports Ca/P inorganique étaient les plus grands dans le cartilage au repos (Cartilage non-différentié hyalin), suggérant un lien initiale entre Ca et les chrondromucoprotéines. Cependant, au début de la calcification, pendant la prolifération du cartilage les rapports Ca/P étaient beaucoup plus petits (ca. 1.50) mais augmentaient graduellement avec l'advancement de la minéralisation. Des changements importants survenaient dans la composition de la phase organique, pendant la calcification endochondrale. Comme il a été déterminé par l'analyse de l'hydroxyproline la quantité de collagéne diminuait progressivement pendant la calcification du cartilage, mais augmentait rapidement pendant la formation d'os. Comme il a été déterminé par l'analyse de l'héxosamine et du sulfute les chrondromucoprotéines étaient aux niveaux les plus éléves pendant la prolifération du cartilage et diminuaient constamment au cours de la calcification. Cependant, bien que la calcification était déja très avancée dans le cartilage hypertrophique, de grandes quantites de mucopolysaccharides étaient encore présentes. Les rapports sulfure/hhéxosamine montraient un léger déclin pendant les premiéres étapes de la calcification, mais augmentaient beaucoup pendant le cours de la minéralisation. Les quantités d'acide sialique étaient plus grandes dans le cartilage de l'épiphyse que dans le cartilage au repos ou dans l'os. Les lipides augmentaient rapidement pendant la calcification du cartilage, mais étaient très réduites dans l'os complètement formé. La signification de ces résultats est discutée.
    Abstract: Zusammenfassung Eine Seziermethode, die eine Schichten-Analyse der Beinepiphysenplatte von Rinderfeten erlaubt, wurde entwickelt. Proben vor und nach Waschen des Gewebes der verschiedenen Schichten werden untersucht in bezug auf Elektrolyte und organische Bestandteile, als auch in bezug auf Dichte, Aschengehalt und Feuchtigkeit. Die Resultate zeigten eine Zunahme des Aschengehaltes und der Dichte, während der Wassergehalt abnahm. Unerwartet hoch waren die Aschenwerte im in Verkalkung begriffenen Knorpel. Ausgedrückt in Prozent Trockengewicht, ergab gewaschener, verkalkter Knorpel den höchsten Wert aller Zonen. In den Frühstadien der Knorpelmineralisation nahm der Natriumgehalt (m Mol/l Frischgewebe) ab, während Ca und anorganischer P zunahmen. Mit fortschreitender Verkalkung erhöhte sich auch der Magnesium-Spiegel, allerdings nur zu einem Bruchteil des Ausmaßes, in welchem Ca und P zunahmen. Die höchsten Ca/P anorg. Verhältnisse wurden im Ruheknorpel (undifferenzierter hyaliner Knorpel) gefunden, was auf eine initiale Bindung von Ca durch Chondromucoproteine hinweist. Die Ca/P-Verhältnisse proliferierenden Knorpels waren jedoch bei Verkalkungsbeginn viel tiefer (ca. 1.50). Diese nahmen allerdings mit fortschreitender Mineralisierung stetig zu. In der endochondralen Verkalkungsphase fanden markante Veränderungen in der Zusammensetzung des organischen Anteils statt. Basierend auf der Hydroxyprolinanalyse nahm der Collagengehalt in der knorpeligen Verkalkungsperiode fortschreitend ab, während er jedoch bei der Knochenbildung rasch zunahm. Die an Hand von Hexosamin- und Schwefelanalysen bestimmten Chondromucoproteingehalte ergaben Höchstwerte im proliferierenden Knorpel und fielen stetig ab mit zunehmender Verkalkung. Trotz der im hypertrophischen Knorpel schon weit fortgeschrittenen Verkalkung waren immer noch große Mengen an Mucopolysacchariden vorhanden. Die Schwefel/Hexosamin-Verhältnisse zeigten eine minimale Abnahme in den frühen Verkalkungsphasen, nahmen jedoch markant zu bei fortschreitender Mineralisation. Der Sialinsäurespiegel war im Epiphysenknorpel, verglichen mit demjenigen des Ruheknorpels oder Knochens, erhöht. In der knorpeligen Verkalkungsphase nahmen die Lipide rasch zu, während jedoch die Werte des vollständig ausgebildeten Knochens stark vermindert waren. Die Bedeutung dieser Ergebnisse wird besprochen.
    Notes: Abstract A dissection procedure has been devised to permit zonal analysis of the epiphyseal plate of fetal calf leg bones. Samples of whole and washed tissue from the various zones were analyzed for their content of electrolyte and organic constituents, as well as for density, ash and moisture. Results showed that as ash content and density increased, water content decreased. Ash levels in calcifying cartilage zones were unexpectedly high. When expressed as a percentage of dry weight, washed calcified cartilage had the highest content of any zone. In the early stages of the mineralization of cartilage, Na content (mmoles/l of fresh tissue) decreased as Ca and inorganic P increased. Magnesium levels increased as calcification proceeded, but only at a fraction of the rate of Ca and P. Ratios of Ca/inorganic P were highest in resting cartilage (non-differentiated hyaline cartilage), suggesting an initial binding of Ca to chondromucoproteins. However, at the onset of calcification in proliferating cartilage, Ca/P ratios were much lower (ca. 1.50), but gradually increased with advancing mineralization. Marked changes occurred in the composition of the organic phase during endochondral calcification. As determined by hydroxyproline analysis, collagen content progressively decreased during cartilaginous calcification, but increased rapidly during bone formation. As determined by hexosamine and sulfur analysis, chondromucoproteins were at highest levels in proliferating cartilage and decreased steadily as calcification increased. However, although calcification was already well advanced in hypertrophic cartilage, large amounts of mucopolysaccharide still were present. Sulfur/hexosamine ratios showed a slight decline during the early stages of calcification, but increased markedly with further mineralization. Sialic acid levels were elevated in epiphyseal cartilage over those in resting cartilage or bone. Lipids increased rapidly during cartilaginous calcification, but were greatly reduced in fully-formed bone. The significance of these findings is discussed.
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  • 3
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    Calcified tissue international 3 (1969), S. 151-162 
    ISSN: 1432-0827
    Keywords: Calcification ; Physiologic ; Phosphonic Acids ; Phosphates ; Crystallization ; Electron Microscopy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé On a étudié la formation de l'hydroxyapatite de calcium cristallin à partir de solutions d'ions de calcium et de phosphate et l'inhibition de la croissance de cristaux de l'hydroxyapatite de calcium au moyen de polyphosphonates et de polyphosphates. Les polyphosphonates, éthane hydroxy-1-diphosphonate-1,1 de disodium et dichlorométhanediphosphonate de disodium, sont inhibiteurs efficaces contre la croissance de cristaux de l'hydroxyapatite de calcium. Les polyphosphates sont aussi inhibiteurs efficaces contre la croissance de cristaux de l'hydroxyapatite de calcium tant que le niveau exigé de polyphosphate intact est présent dans le système. Cependant, à cause de leur instabilité hydrolytique, qui est soulignée par une température élevée, valeur de pH basse, et certaines enzymes, la concentration du polyphosphate diminue avec le tempsin vitro, et son activité comme inhibiteur est perdue. Au contraire aux polyphosphates, les polyphosphonates sont hydrolytiquement stables. Les polyphosphonates sont chimiosorbés sur la surface des microcristallites de l'hydroxyapatite de calcium, ainsi empêchant l'occurrence d'autre croissance de cristaux semblable à l'action d'autres poisons connus de croissance de cristaux. On propose l'extension de cette action sur la formation de l'apatite et cette stabilité des polyphosphonates aux applications médicales et dentaires concernant le metabolisme pathologique de calcium et de phosphate.
    Abstract: Zusammenfassung Die Bildung des kristallinen Calciumhydroxyapatit aus Lösungen, welche Calcium- und Phosphationen enthalten, und die Hemmung der Bildung von kristallinen Calciumhydroxyapatit durch Polyphosphonate und Polyphosphate wurden untersucht. Polyphosphonate, Dinatriumäthan-1-hydroxyl-1,1-diphosphonat und Dinatriumdichloromethandiphosphonate verhindern das Kristallwachstum des Calciumhydroxyapatits. Die Polyphosphate verhindern ebenfalls das Kristallwachstum des Calciumhydroxyapatits, solange die notwendige Konzentration des nicht hydrolysierten Polyphosphats vorhanden ist. Wegen ihrer hydrolytischen Unbeständigkeit, die durch hohe Temperatur, niedrige pH und bestimmte Enzyme erhöht wird, vermindert sich jedoch die Konzentration des Polyphosphats allmählichin vitro, und ihre Hemmungsaktivität geht verloren. Im Gegensatz zu den Polyphosphaten sind die Polyphosphonate hydrolytisch beständig. Die Polyphosphonate werden an der Oberfläche der Mikrokristallite des Calciumhydroxyapatits chemisorbiert und verhindern, wie andere bekannte Kristallwachstumsgifte, auf diese Weise weiteres Kristallwachstum. Die Beständigkeit der Polyphosphonate und ihre Chemisorption an dem Apatit empfehlen ihren Gebrauch in der ärztlichen und zahnärztlichen Praxis, soweit sie den pathologischen Calcium- und Phosphatstoffwechsel betreffen.
    Notes: Abstract The formation of crystalline calcium hydroxyapatite from solutions of calcium and phosphate ions and the inhibition of calcium hydroxyapatite crystal growth by polyphosphonates and polyphosphates have been studied. The polyphosphonates, disodium ethane-1-hydroxy-1,1-diphosphonate and disodium dichloromethane diphosphonate, are effective inhibitors of calcium hydroxyapatite crystal growth. The polyphosphates are also effective inhibitors of calcium hydroxyapatite crystal growth as long as the required level of intact polyphosphate is present in the system. However, because of their hydrolytic instability, which is enhanced by high temperature, low pH, and certain enzymes, the concentration of the polyphosphate decreases with timein vitro, and its activity as an inhibitor is lost. In contrast to the polyphosphates, the polyphosphonates are hydrolytically stable. The polyphosphonates are chemisorbed on the surface of the microcrystallites of calcium hydroxyapatite and, in the manner of other known crystal growth poisons, thus prevent further crystal growth. The stability of the polyphosphonates and their chemisorption on apatite suggest their use in medical and dental applications involving pathological calcium and phosphate metabolism.
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  • 4
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    Calcified tissue international 3 (1969), S. 184-193 
    ISSN: 1432-0827
    Keywords: Mitochondria ; Calcification ; Calcium ; Chondrocytes ; Growth plate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé Des cultures d'épiphyse prélevées sur des rats et des souris ont été étudiées sous le microscope électronique. Un profile de granules mitochondriques de densité électronique a été trouvé. Les chondrocytes dans la zone proliférative avaint peu de granules, alors que ceux des zones successives ont montré une augmentation progressive de leur nombre et densité jusqu'à ce que la zone de calcification provisoire ait été atteinte. Cette zone a montré une distribution périphérique de mitochondries et une réduction du nombre et de la densité des granules mitochondriques. Du calcium isotopique 47 a été utilisé autoradiographiquement pour déterminer la location de calcium dans ces cellules. Des grains ont été trouvés sur les membranes R.E. et sur la plupart des mitochondries. La preuve d'un profile de ces granules et de leur rapport spatial avec la face de minéralisation indique une action éventuelle de mitochondries dès le début de la calcification de la matrice.
    Abstract: Zusammenfassung Epiphysekulturen von Ratten und Mäusen wurden unter dem Elektronenmikroskop untersucht. Ein Profil von mitochondrischen Körnchen mit elektronischer Dichte wurde gefunden. Chondrozyten in der Proliferationszone wiesen wenig Körnchen auf, während die der nachfolgenden Zonen allmählich an Zahl und Dichte zunahmen, bis die Zone der provisorischen Verkalkung erreicht wurde. Diese Zone zeigte eine periphere Verteilung der Mitochondrien und eine Abnahme in Zahl und Dichte der mitochondrischen Körnchen. Isotopes Kalzium 47 wurde autoradiographisch verwendet, um die Lage des Kalziums in diesen Zellen zu bestimmen. Körnchen wurden auf den E.R.-Membranen und auf einem Großteil der Mitochondrien gefunden. Der Nachweis eines Profils dieser Körnchen und ihres räumlichen Verhältnisses zur Mineralisierungsfläche weist auf einen möglich Einfluß der Mitochondrien mit Beginn der Matrixverkalkung hin.
    Notes: Abstract Rat and mice epiphyseal growth plates were studied with the electron microscope. A gradient of mitochondrial electron-dense granules was found. Chondrocytes in the proliferative zone had few granules, while those of the succeeding zones showed a gradual increase in number and density until the zone of provisional calcification was reached. This zone showed a peripheral distribution of mitochondria and a decrease in the number and density of mitochondrial granules. Isotopic47calcium was used autoradiographically to determine the location of calcium in these cells. Grains were found over the endoplasmic reticulum membranes and over most mitochondria. The demonstration of a gradient of these granules and their spatial relation to the mineralization front suggests a possible involvement of mitochondria in the onset of matrix calcification.
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  • 5
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    Calcified tissue international 4 (1969), S. 78-83 
    ISSN: 1432-0827
    Keywords: Bone ; Calcification ; Osteomalacia ; Phosphorus ; Vitamin D
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé Les effects d'une dose de 1 mg de vitamine D3 (40 000 Unités,) administrée par voie intra-veineuse, ont été étudiés sur l'histologie osseuse et le métabolisme du phosphore chez 19 sujets contrôles dont l'histologie était normale et 28 malades présentant les caractères histologiques de l'ostéomalacie par carence vitaminique D. L'administration de la vitamine D n'a entraîné aucune modification histologique ou biologique significative chez les sujets contrôles. Mais chez les ostéomalaciques, il est apparu en moins de sept jours une augmentation très significative du front de calcification à l'interface tissue-ostéoïde-tissue-calcifié. Cette modification s'accompagnait d'une ascension progressive de la phosphatémie et de la réabsorption tubulaire du phosphore atteignant dans le même délai des valeurs normales.
    Abstract: Zusammenfassung Bei 19 Patienten mit normaler Knochenhistologie und bei 28 Patienten mit histologisch gesicherter Osteomalacie wurde die Wirkung von 1 mg Vitamin D3 (40000 Iv) i.v. auf die Knochenhistologie und den Phosphatmetabolismus untersucht. Bei den Kontrollpatienten konnten keine signifikanten Änderungen nach Vitamin D festgestellt werden, wogegen die Osteomalacie-patienten innerhalb von 7 Tagen eine deutliche Zunahme der Verkalkungszone an der Grenze zwischen Osteoid- und Knochengewebe zeigten. Diese Änderung war von einer fortschreitenden Zunahme des Serum-Phosphates, verbunden mit einer gesteigerten renalen tubulären Rückabsorption des Phosphates begleitet; beide kehrten anschließend gleichzeitig wieder zur Norm zurück.
    Notes: Abstract The effect of a 1 mg dose of intravenous Vitamin D3 (40,000 i.u.) on bone histology and phosphate metabolism was investigated in 19 patients with normal bone histology and 28 patients with histological evidence of osteomalacia. No significant changes occurred in the control patients after Vitamin D but the patients with osteomalacia showed a marked increase, within seven days, in the proportion of osteoid having a calcification front. This was accompanied by a progressive rise in the serum phosphate, which was associated with an increase in the renal tubular reabsorption of phosphate to normal.
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  • 6
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    Calcified tissue international 4 (1969), S. 231-244 
    ISSN: 1432-0827
    Keywords: Calcification ; Pyrophosphate ; Inhibitors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé Les propriétés d'induction de calcification des liquides biologiques peuvent être mesurées, in vitro et in vivo, par leur possibilité de redurcir des blocs d'émail décalcifié. Cette propriété est exprimée par les concentrations de calcium (et de phosphate) de solutions synthétiques inductrices de calcification, de concentrations et d'activité connues. Un plasma humain typique a une activité inductrice correspondant à celle d'une solution contenant du calcium, 0,70 mM, Ca/P, 1,67 et fluorure, 0,05 mM. L'activité relativement peu élevée des sérums et des plasmas s'explique par la présence d'inhibiteurs ioniques. L'ion phosphate est l'un d'eux, mais ne peut rendre compte de l'inhibition totale. Des anions et des cations sont responsables de l'inhibition, avec un rôle majeur pour les cations. Les ions suivants, en concentration physiologique, jouent un rôle inhibiteur: P7O 7 4− , HCO 3 − , SiO 4 2− , CrO 4 2− , Mg2+, Zn2+. Un mélange de ces ions provoque une inhibition totale identique à celle du plasma.
    Abstract: Zusammenfassung Der Einfluß biologischer Flüssigkeiten auf den Verkalkungsvorgang kann in vitro und in vivo anhand ihrer Fähigkeit, enthärtete Blöcke von Zahnschmelz wieder zu härten, gemessen werden. Diese Aktivität wird ausgedrückt als Konzentration des Calciums (und Phosphates) synthetischer calcifizierender Lösungen mit bekannter Konzentration und Aktivität. Die Aktivität eines charakteristischen menschlichen Plasmas entsprach derjenigen einer Lösung folgender Zusammensetzung: Calcium 0,70 mM; Ca/P=1,67 und Fluorid 0,05 mM. Die relativ niedrige Aktivität von Serum und Plasma ist bedingt durch das Vorhandensein einer Anzahl ionischer Inhibitoren. Das Pyrophosphation ist ein solcher; er kann aber nicht für die gesamte Inhibition verantwortlich gemacht werden. Sowohl anionische als auch kationische Inhibitoren sind vorhanden, wobei die Kationen den Hauptanteil ausmachen. Folgende Ionen erwiesen sich in einer physiologischen Konzentration als Inhibitoren synthetischer Systeme: P7O 7 3− , HCO 3 − , SiO 4 1− , CrO 4 2− , Mg2+, Zn2+. Zusammengenommen verursachten diese Ionen eine Gesamtinhibition ähnlich derjenigen des Plasmas.
    Notes: Abstract The calcifying activities of biological fluids can be measured,in vitro andin vivo, by their ability to reharden softened blocks of tooth enamel. The activity is expressed in terms of the calcium (and phosphate) concentrations of synthetic calcifying solutions of known concentration and activity. A typical human plasma had an activity corresponding to that of a solution of the following concentration: calcium, 0.70 mM; Ca/P, 1.67 and fluoride, 0.05 mM. The relatively low activity of serums and plasmas was shown to arise from the presence of a number of ionic inhibitors. Pyrophosphate ion is one such inhibitor but cannot account for the major inhibition. Both anionic and cationic inhibitors were shown to be present, with the cations respresenting the major portion. The following ions at their reported physiological concentration were shown to be inhibitors in synthetic systems: P7O 7 4− , HCO 3 − , SiO 4 2− , CrO 4 2− , Mg2+, Zn2+. In combination, these ions caused a total inhibition similar to those for plasmas.
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  • 7
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    Calcified tissue international 3 (1969), S. 266-273 
    ISSN: 1432-0827
    Keywords: Calcification ; Arteries ; Membranes ; Elastic tissue
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé Avec la modification d'une méthode de von Kossa nous avons macroscopiquement representé les dessins de calcification de la membrane élastique intérieure, ainsi que les grosses artères du bassin, des artères des extrémités inferieures, des artères du bras, de la rate et des reins. Dans les artères du type élastique, dans les A.a. ilicae communes et internae, se présentaient les dégénérations calcaires de la membrane élastique intérieure sous forme d'incrustations noires arrondies ou polygonales qui ont été formes en groupes. Elles étaient toujours présentes chez des enfants agés de plus de trois mois et chez des aux adultes. Dans les artères musculaires, se montraient les parties calcifiées de la membrane élastique intérieure en forme de «bandes de calcaire» noires et groupes en paires le long des bordures des fissures de la membrane. Dans le cas où existait une calcinose forcée, on pouvait montrer avec cette méthode tout le système de fissures de la mambrane élastique intérieure. Chez tous les morts âgés de 10 à 20 ans, nous avons trouvé des bandes de calcaire dans les artères musculaires des extrémités inferieures. Ces bandes de calcaire ont été constatées aussi dans des personnes plus âgées. Au point de la fusion des bandes de calcaire et des incrustations calcaire polygonales des dépôts calcaires en forme de feuille («feuilles de calcaire») se forment dans la membrane elastique. Les bandes de calcaire et les feuilles de calcaire représentent des points de cristallisation pour des dépôts calcaire granuleux. Ils se forment dans la plupart des cas sur le la côté externe tourné vers la media.
    Abstract: Zusammenfassung Mit einer modifizierten von Kossa-Methode wurden die Verkalkungsmuster der inneren elastischen Membran der großen Beckenarterien, der Arterien der unteren Extremität, der Oberarm-, Milz-und Nierenarterien makroskopisch dargestellt. In den Arterien vom elastischen Typ, i.e. in den Aa. ilicae communes et internae, erschienen die Verkalkungen der inneren elastischen Membran als schwarze rundliche oder polygonale Inkrustationen, die zu Gruppen angeordnet waren. Sie wurden häufig bereits bei Neugeborenen festgestellt. Bei Kindern, die älter waren als 3 Monate und bei Erwachsenen lagen sie stets vor. — In den muskulären Arterien traten die verkalkten Anteile der inneren elastischen Membran makroskopisch als schwarze paarweise angeordnete „Kalkbänder” entlang den Rändern vorgebildeter Membranspalten auf. Bei ausgeprägter Calcinose konnte mit der angewandten Methode das gesamte Spaltensystem der inneren elastischen Membran dargestellt werden. Kalkbänder wurden in den muskulären Arterien der unteren Extremität bei allen 10–20 Jahre alten Verstorbenen vorgefunden und waren auch in den nachfolgenden Altersstufen stets vorhanden. Beim Zusammenfluß von Kalkbändern und polygonalen Kalkinkrustationen entstehen in der inneren elastischen Membran folienartige Kalkablagerungen („Kalkfolien”). Die Kalkbänder und Kalkfolien stellen Kristallisationspunkte für körnige Kalkablagerungen dar, die zumeist an ihrer äußeren, der Media zugekehrten Seite entstehen.
    Notes: Abstract Calcification patterns of the internal elastic membrane of the main pelvic arteries, lower limb arteries, brachial, splenic and renal arteries were demonstrated grossly by a modified von Kossa technique. In the elastic segment in the common and internal iliac arteries, the membrane calcification appeared as groups of roundish or polygonal incrustations. They were found frequently in newborns, and were always present in infants of more than three months, as well as in adults. In the muscular arteries, the calcified parts of the internal elastic membrane appeared grossly as pairs of bands (“calcific bands”) along the edges of the pre-existing gaps in this membrane. When calcification was pronounced, the whole pattern of the membrane gaps could be demonstrated by the method used in this study. Calcific bands were found in the muscular arteries of the lower limbs in all 10–20 year-old subjects, and were always present in the older age groups. The confluence of calcific bands or polygonal membrane incrustations found in the iliac arteries lead to sheet-like membrane calcification. The calcific bands and sheets represent crystallizing points for grain-like calcific deposits, which appear later on the medial surface.
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    Calcified tissue international 3 (1969), S. 363-365 
    ISSN: 1432-0827
    Keywords: Calcification ; Mitochondria ; Protozoa
    Source: Springer Online Journal Archives 1860-2000
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    Calcified tissue international 3 (1969), S. 38-54 
    ISSN: 1432-0827
    Keywords: Epiphyseal cartilage ; Calcification ; Apatite crystals ; Organic/Inorganic relationships
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé Les rapports entre composants organiques et inorganiques du cartilage ont été étudiés au niveau des épiphyses tibiales chez des rats de 5 jours et au niveau des jonctions costo-chondrales chez des cobayes d'un mois. Voici les principaux résultats auxquels on est parvenu: (a) Dans les zones où la calcification s'amorce les cristallites d'apatite sont susceptibles d'être facilement éliminés des coupes en araldite et en glycol methacrylate (GMA) après traitement pendant une heure par une solution d'acide formique au 2%. (b) Les zones décalcifiées sont douées d'une faible densité aux électrons et vont exemptes d'une structure quelconque. Seulement la fixation à l'osmium peut révéler du matériel amorphe. (c) Indépendemment du fixateur et du moyen d'inclusion, les coupes décalcifiées, traitées par l'acétate d'uranyl et/ou par le citrate de plomb, montrent de fines structures allongées dont l'aspect est semblable à celui des cristallites. (d) Ces structures ainsi qu'un fond dense interposé prennent l'acide phosphotungstique (PTA) dans les coupes en GMA, une méthode celle-ci qui met en évidence les polysaccharides. (e) Le fond dense ne prend plus le PTA après traitement par la hyaluronidase et en même temps les structures semblables au cristallites apparaissent plus faibles. Après traitement par l'acétate d'uranyl et le citrate de plomb, l'attaque par la hyaluronidase ne produit aucune modification appréciable. Au contraire l'aspect des structures semblables aux cristallites apparait modifié par la digestion à la papaïne. (f) Quand la décalcification à l'EDTA précéde l'enrobage, des amas de matériel fibrillaire se mettent en évidence dans les zones où la calcification s'était amorcée. L'ensemble de ces résultats permet d'établir la nature organique des structures semblables au cristallites et porte aussi à admettre que celles-ci soient formées par de fins filaments cylindriques (digérés par la papaïne) entourés, et probablement engainés par del polysaccharides (digérés par la hyaluronidase et prennant le PTA dans les coupes en GMA).
    Abstract: Zusammenfassung Die Wechselbeziehungen zwischen den organischen und inorganischen Substanzen des verkalkenden Knorpels wurden in der tibialen und femuralen Epiphyse 5 Tage alter Ratten und in den Rippen 1 Monat alter Meerschweinchen untersucht. Die Hauptergebnisse waren: a) Die Hydroxyapatitkristalle der Frühverkalkungszonen können in Araldit- wie auch in Glycolmethylacrilatschnitten (GMA) mit einer lstündigen Behandlung durch 1% ige Ameisensäure leicht entfernt werden. b) Die entkalkten Zonen haben eine sehr niedrige Elektronendichte und enthalten keine sichtbaren Festkörper. Nach Fixierung mit Osmiumsäure kann man darin ein formloses Material erkennen. c) Eine Färbung der Schnitte mit Uranacetat und Bleicitrat, welche von den Fixier- und Einbettungsmitteln nicht beeinträchtigt wird, zeigt feine, längliche Körper (“Kristallgeister”) an, welche morphologisch den Kristallen von Hydroxyapatit gleichen. d) Die Färbung der GMA-Schnitte mit Phosphowolframsäure (PWS), eine Methode welche Polysaccharide anzeigt, hob diese “Kristallgeister” besonders hervor und demonstrierte auch eine dichte dazwischenliegende Grundsubstanz. e) Diese Substanz ist nach Behandlung mit Hyaluronidase nicht mehr färbbar mit PWS; die Färbbarkeit der “Kristallgeister” wird dabei jedoch nur verringert. Die Hyaluronidasebehandlung verändert die Uranacetat- und Bleicitratfärbung nicht. Die Feinstruktur der “Kristallgeister” wird durch Papainbehandlung sehr angegriffen. f) Falls die Schnitte vor dem Einbetten mit EDTA entkalkt werden, können Faserbündel in den Frühzonen der Verkalkung nachgewiesen werden. Diese Ergebnisse bestätigen die organische Natur der “Kristallgeister”. Sie beweisen auch, daß dieselben aus feinen Proteinstäbchen bestehen (verdaulich in Papain) und von Polysacchariden umgeben und vielleicht auch überzogen sind (verdaulich in Hyaluronidase und anfärbbar mit PWS).
    Notes: Abstract The organic/inorganic relationships in calcifying cartilage have been studied in tibialfemoral epiphyses of 5-day-old rats and in costochondral junctions of 1-month-old guinea pigs. The main results are: (a) Apatite crystallites in areas of early cartilage calcification are easily removed from araldite and glycol methacrylate (GMA) sections by 1-hour treatment with 2% formic acid. (b) The decalcified areas have a very low electron density and do not contain recognizable structures. Only after osmium fixation can an amorphous material be found in them. (c) Independently from the fixative and the embedding medium, staining decalcified areas with uranyl acetate and/or lead citrate reveals thin, elongated structures (crystallite ghosts) similar in shape to apatite crystallites. (d) These crystallite ghosts and a dense background are stained by phosphotungstic acid (PTA) in GMA sections, a method which reveals polysaccharides. (e) The dense background is no longer stained by PTA after hyaluronidase digestion and the stainability of the crystallite ghosts is reduced. After uranyl acetate/lead citrate staining there are no recognizable changes due to hyaluronidase. But, on the other hand, the fine structure of the crystallite ghosts is modified by papain digestion. (f) Clusters of fibrillar material are present in the areas of early calcification when EDTA decalcification is carried out before embedding the specimens. These results confirm the organic nature of the crystallite ghosts and suggest that they are formed by thin, rod-like protein/like structures (digested by papain) surrounded, and probably sheathed, by acid polysaccharides (digested by hyaluronidase and stained by PTA in GMA sections).
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    Calcified tissue international 4 (1969), S. 136-146 
    ISSN: 1432-0827
    Keywords: Bone ; Calcification ; Osteoblasts ; Osteoclasts ; Poultry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé L'activité des cellules osseuses et la composition du fémur de pondeuses furent examinées pendant sept jours de déficience calcique (diète contenant 0,13% de calcium) et sept jours de réplétion (diète contenant 3,2% de calcium). Du point de vue histologique, seul l'os cortical donnait des signes nets de résorption et d'activité ostéoclastique. Le nombre d'ostéoclastes dans l'os médullaire différait peu des valuers témoin pendant les périodes de déficience et de réplétion subséquente, sauf pour une augmentation significative au premier jour de déplétion. L'effect histologique le plus important dans l'os médullaire était une augmentation marquée en nombre d'ostéoblastes aux troisième, cinquième, et un peu moins au septième jours de déplétion. Le nombre d'ostéoblastes était en corrélation positive avec la teneur de l'os médullaire en ostéoide et négative avec son degré de calcification. L'activité de l'os médullaire en phosphatase alcaline augmentait avec la longueur de la déficience calcique. Un jour après le retour des pondeuses à une diète contenant 3,2% de calcium, la calcification de l'os médullaire avait augmenté de façon significative, le nombre d'ostéoblastes avait diminué au niveau ou au-dessous du niveau de contrôle et l'activité de la phosphatase alcaline avait baissé considérablement. L'importance de ces résultats est discutée par rapport au controle des populations des cellules dan l'os et au rôle de l'os médullaire.
    Abstract: Zusammenfassung Die Zahl der Knochenzellen und die Zusammensetzung des Femurs von Legehennen wurden während einer siebentägigen Calciumentzugsperiode (Calciumgehalt des Futters 0,13%) und einer siebentägigen Ersatzperiode (Calciumgehalt des Futters 3,2%) untersucht. Histologisch zeigte nur die Cortex eindeutige Knochenresorption und osteoklastische Aktivität. Abgesehen von einer signifikanten Zunahme am 1. Tag des Calciumentzuges, variierte die Zahl der Osteoklasten im Markknochen sowohl während der Entzugs- als auch während der nachfolgenden Ersatzperiode wenig. Die wichtigste histologische Änderung im Markknochen bestand in einer starken Zunahme in der Zahl der Osteoblasten am 3., 5. und etwas weniger am 7. Tag der Entzugsperiode. Die Zahl der Osteoblasten zeigte eine positive Korrelation mit dem Osteoidgehalt des Markknochens und eine negative mit dem Grade seiner Verkalkung. Die Aktivität der alkalischen Phosphatase im Markknochen war desto größer je länger den Hennen die calciumarme Ration verfüttert worden war. Die Wiederverabreichung der Ration, welche 3,2% Calcium enthielt, verursachte innerhalb eines Tages eine signifikante Zunahme in der Verkalkung des Markknochens, ein Absinken der Osteoblastzahl auf die Kontrollwerte oder unter sie und eine drastische Verringerung der alkalischen Phosphataseaktivität. Die Bedeutung dieser Ergebnisse in bezug auf die Kontrolle des Knochenzellenbestandes und auf die Funktion des Markknochens wird diskutiert.
    Notes: Abstract Bone cell activity and the composition of the femur of laying hens were studied during 7 days of calcium depletion on a 0.13% calcium diet and 7 days of calcium repletion on a 3.2% calcium diet. Histologically, only cortical bone showed clear signs of bone resorption and osteoclastic activity during the depletion period. The number of osteoclasts in medullary bone varied little from control values throughout both calcium depletion and repletion, except for a significant increase on the first day of depletion. The major histologicalchange in medullary bone was a marked increase in the number of osteoblasts on the third, fifth and, to a lesser extent, seventh, day of depletion. The number of osteoblasts in medullary bone was positively correlated with its osteoid content and negatively correlated with its degree of calcification. Alkaline phosphatase activity of medullary bone increased with the time the hens had been on the calcium-deficient diet. Returning the hens to the 3.2% calcium ration caused, within one day, a significant increase in medullary bone calcification, a decrease of osteoblast numbers to, or below, control levels, and a drastic reduction in alkaline phosphatase activity of medullary bone. The significance of these findings in relation to the control of bone cell populations and the functions of medullary bone is discussed.
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    Calcified tissue international 4 (1969), S. 101-112 
    ISSN: 1432-0827
    Keywords: Calcification ; Ligament ; Mollusc ; Aragonite
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Une étude de microscopie électronique est réalisée sur la formation et la structure du ligament interne deMytilus edulis etPinctada radiata. Cette partie du ligament est dérivée des cellules isthmiques qui sont de forme cylindrique irrégulière. Elles présentent un ergastoplasme bien développé et un appareil de Golgi, engagé dans l'élaboration de vésicules et granules qui s'incorporent au niveau de la conchioline. Les cristaux se forment au niveau du front de calcification, à la surface interne du ligament. Ils sont entourés par une enveloppe. Ils se présentent comme des monocristaux d'aragonite, allongés et en forme d'aiguilles, dispersés dans le ligament. Bien que les constituants de la carapace et du ligament soient identiques, il existe des différences concernant l'augmentation quantitative de conchioline et une diminution en nombre, forme diverse, groupement et croissance des cristaux. Ces différences sont probablement liées à la fonction spécialisée du ligament.
    Abstract: Zusammenfassung Die Bildung und Struktur des inneren Ligamentes vonMytilus edulis undPinctada radiata wurden am Elektronenmikroskop untersucht. Dieser Teil des Ligamentes stammt von den Isthmuszellen ab, deren Form unregelmäßig säulenartig ist. Sie zeigen ein vorspringendes, rauhes endoplasmatisches Reticulum und einen Golgiapparat, welche sich mit der Bildung von Bläschen und Granula befassen, die schließlich in einem integralen Teil des Conchiolins eingebaut werden. Die Kristalle entstehen an der Calcifikationsgrenze an der inneren Oberfläche des Ligamentes und sind in Hüllen eingeschlossen. Sie bestehen aus langen, nadelförmigen, einzelnen Aragonit-Kristallen, die über das ganze Ligament verteilt sind. Obschon die Bestandteile der Muschel und des Ligamentes gleichartig sind, unterscheiden sich die beiden durch eine erhöhte conchiolinmenge, wie auch durch eine Abnahme der Anzahl der Kristalle, welche verschieden in der Form, in der Anordnung und im Wachstum sind. Dies alles ist vermutlich auf die spezielle Funktion des Ligamentes zurückzuführen.
    Notes: Abstract An electron microscope study was made of the formation and structure of the inner ligament ofMytilus edulis andPinctada radiata. This part of the ligament is derived from the isthmus cells which are irregular columnar in shape. They exhibit a prominent rough endoplasmic reticulum and a Golgi apparatus, which are concerned with the elaboration of vesicles and granules eventually incorporated into an integral part of the conchiolin. The crystals arise at the calcification front at the inner surface of the ligament and are enclosed in envelopes. They consist of long, needle-shaped, single aragonite crystals widely dispersed in the ligament. Although the components of the shell and ligament are similar, differences between them consist of an increased amount of conchiolin, as well as a decrease in the amount, diversity of form, arrangement and growth of the crystals; all probably related to the specialized function of the ligament.
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    Calcified tissue international 4 (1969), S. 359-365 
    ISSN: 1432-0827
    Keywords: Metals ; Ions ; Buffers ; Calcification
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé L'action de divers ions métalliques polyvalents sur les propriétés métastables d'un tampon calcifiable a été étudiée. A des concentrations de 1 μM ou moins, les ions Pb2+, F2+, Fe3+, Cr3+, Bi3+ et Al3+ déstabilisent le tampon. Il semble que les phosphates insolubles formés par ces ions déclanchent la précipitation de l'apatite. L'importance de ces résultats dans l'étiologie des calcifications pathologiques et la calciphylaxie est décrite.
    Abstract: Zusammenfassung Die Wirkung von verschiedenen polyvalenten Metallionen auf die Metastabilität eines Calcifikationspuffers wurde untersucht. Bei Konzentrationen von 1 μM oder weniger wird der Puffer durch Pb2+, Fe2+, Fe2+, Cr3+, Bi3+ und Al3+ entstabilisiert. Die Resultate lassen vermuten, daß unlösliche Phosphate, die mit diesen Ionen entstehen, eine Fällung von Apatit veranlassen. Die Bedeutung dieser Befunde bei pathologischen Verkalkungen und Calciphylaxis werden besprochen.
    Notes: Abstract The effect was studied of various polyvalent metal ions on the metastability of a calcification buffer. At concentration of 1 μM or less, Pb2+, Fe2+, Fe3+, Cr3+, Bi3+ and Al3+ ions were found to destabilize the buffer. The results suggest that insoluble phosphates formed by these ions initiate the precipitation of calcium apatite. The implications of these findings to pathological calcification and calciphylaxis are discussed.
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    Calcified tissue international 4 (1969), S. 39-47 
    ISSN: 1432-0827
    Keywords: Dehydroepiandrosterone ; Calcification ; Embryo ; Tissue Culture ; Bone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Physics
    Description / Table of Contents: Résumé Les modes d'utilisation de glucose, le contenu de calcium et d'hydroxyproline et la densité cellulaire du perioste de les os frontaux d'embryons de poulet de 12 et 13 jours de developpement, cultivés sur coagulum de plasma, se presentant différenment à chaque âge. Cultivés avec sulfate de déhydroèpiandrostérone en concentration 1 mM, les frontaux de 12 jours montrent un synthese augmentée du matrice osseuse, celle de 13 jours se calcifient à une vélocité significativement plus grande que celle des os contôles. Le degré de calcification au quatrième jour de culture measuré par la relation calcium/hydroxyproline, suit un fonction lineáire avec le logarithme des doses de sulfate de dehydroepiandrostérone employées (0.5, 1,0 et 2,0 mM). Les renseignements obtenus indiquent que les frontaux de 13 jours, cultivés “in vitro” constituent modeles experimentaux appropriés pour étudier l'effet des androgénes sur le tissue osseux.
    Abstract: Zusammenfassung Stirnbeine von Hühnerembryonen an ihrem 12. und 13. Entwicklungstag entnommen und in vitro kultiviert zeigen verschiedene Arten der Glucoseverwertung der Periostzellendichte, des Calcium- und Hydroxyprolingehaltes. Wird Dehydroepiandrosteronsulfat dem Medium in einer 1 mM-Konzentration zugegeben, so beteiligen sich die 12tägigen Stirnbeine vorwiegend an der Knochengewebesynthese, während die 13tägigen signifikant stärker verkalken als die Kontrollen. Gemessen an der Calcium/hydroxyprolin Ratio bildet die Verkalkung der 13tägigen Stirnbeine eine lineare Funktion mit den Logarithmen der verwendeten Dosen von Dehydroepiandrosteronsulfat (0,5, 1,0 und 2,0 mM). Das in vitro kultivierte 13tägige Stirnbein schein ein geeignetes Experimentiermodell zur Studie der Dehydroepiandrosteronsulfatwirkung auf das Knochengewebe zu sein, weil es das grundlegende Phänomen (erhöhte Verkalkung) wiedergibt, welches man auch bei mit Androgenen behandelten Menschen und Tieren beobachtet.
    Notes: Abstract Chick embryo frontal bones at 12 and 13 days of development cultivatedin vitro exhibit different patterns of glucose utilization, periosteal cellular density and calcium and hydroxyproline content. When dehydroepiandrosterone sulfate is added to the medium at a concentration 1 mM, 12-day frontals engage primarily in osteoid tissue synthesis while 13-day frontals calcify at a significantly greater rate than controls. Measured with the ratio calcium/hydroxyproline, the calcification of 13-day frontals follows a linear function with the logarithm of the doses of dehydroepiandrosterone sulfate employed (0.5, 1.0 and 2.0 mM). The 13-day frontal bone cultivatedin vitro seems to be an adequate experimental model for the study of the effects of dehydroepiandrosterone sulfate on bone tissue because it reproduces the basic phenomenon (increased calcification) observed in man and animals treated with androgens.
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    International Journal of Quantum Chemistry 3 (1969), S. 131-139 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analytical approximation for the hypersurface E (pr-approximation) is given using the two- and three-center-functions pλμ and rμνλ, which is valid for any number N of atoms and is invariant with respect to the number of centers in its analytical structure (rule of construction). This is valid too if N is reduced either by the association of atoms or by transitions to infinity. pλμ can be fixed by two-center-systems. But rμνλ is still free except for the fulfilling of some simple requirements. The rule of construction proposed for E is an example for using so-called analytical computers.
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    International Journal of Quantum Chemistry 3 (1969), S. 149-167 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The general formulas which are convenient for cluster analysis of a configuration interaction wave function are presented. These formulas are then used for cluster analysis of the “complete” configuration interaction wave functions of the π-electronic models of benzene and butadiene obtained with a semiempirical method of the Pariser-Parr-Pople type using three different parameterizations. For butadiene the calculations are carried out with Hückel, Hartree-Fock, and Brueckner molecular orbitals. The results clearly indicate that Sinanoǧlu's statement [1, 2], concerning the relative unimportance of the linked parts of the tetraexcited state coefficients in the ci expansion, is justified for these delocalized systems.
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    International Journal of Quantum Chemistry 3 (1969), S. 219-224 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Some calculations are presented on the hydrogen bond using a perturbation theory approach. Results confirm indications of earlier work that perturbation theory is capable of giving a reasonable description of hydrogen bonded systems.
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    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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    International Journal of Quantum Chemistry 3 (1969) 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
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    International Journal of Quantum Chemistry 3 (1969), S. 297-301 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The expansion of the wave function for the 23S state of the two-electron atom in the neighbourhood of the singularity at r1 = r2 = 0 is considered. The restrictions imposed on the variational functions by this expansion are discussed. For the 23S state of He, Li+, N5+ the behaviour of the variational function based on the Fock expansion in the neighbourhood of this singularity is investigated. The agreement of the variational coefficients with the theoretical coefficients is satisfactory. The calculated values of E and 〈δ(r2)〉 for He, Li+, N5+ are given.
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    International Journal of Quantum Chemistry 3 (1969), S. 317-325 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A method of calculating the energy of the long-range interaction between atoms and charges is presented. Simplification of the solution of the perturbation equations is achieved by a formal use of the “Double-Perturbation Method”. Numerical results for the energies of the 2pσ state of HeH+2 are obtained.
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    International Journal of Quantum Chemistry 3 (1969) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 22
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    International Journal of Quantum Chemistry 3 (1969), S. 445-483 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An earlier analysis of the canonical form of a pair of invertible operators obeying the exchange rule \documentclass{article}\pagestyle{empty}\begin{document}$$ AB = \omega BA $$\end{document} is extended to cover a set of operators, between each pair of which a relation of this type exists; and for which a power of each operator is the unit matrix. Such relations define a system which may be regarded as a generalization of the Dirac matrices of relativistic quantum mechanics. We concentrate upon the group theoretic aspects of such a system and its matrix representations. Applications arise from the fact that all projective representations of finite abelian groups take the form of a Dirac Group. In particular, the representations of the magnetic space groups, which are projective representations of the lattice groups, arise in this manner.
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  • 23
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    International Journal of Quantum Chemistry 3 (1969), S. 13-15 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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  • 24
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Notes: The π-electronic properties of furan, oxazole, benzofuran, benzoxazole, anthranil, and dibenzofuran are calculated by the semiempirical self-consistent-field molecular orbital method. A single set of parameters is found which satisfactorily reproduces the π → π* electronic transition energies and other π-electronic properties.
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  • 25
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    International Journal of Quantum Chemistry 3 (1969), S. 67-71 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Alternatives to the Mulliken method of partitioning the overlap charge density in self-consistent charge molecular-orbital calculations are examined. It is found that more realistic methods may lead to significantly different self-consistent charges, and different ordering of the electronic energy levels.
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  • 26
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    International Journal of Quantum Chemistry 3 (1969), S. 621-634 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Generalizing the method of Hirschfelder, Curtiss and Bird for the calculation of the polarizability of molecules, we have calculated both the diagonal and off-diagonal polarizability tensor elements of the nucleotide bases and base pairs. In the course of calculations also the components of the permanent dipole moments have been computed for these systems.On the basis of the results obtained we have determined also the critical field strengths necessary to break off a base pair and thus to induce the unwinding of the DNA double helix. According to the data obtained, a field strength of the order 108 V/cm can induce the unwinding of DNA if its direction lies in the plane of the base pairs.
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  • 27
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    Notes: The electronic spectrum of biphenylene has been studied theoretically. The investigation is based on the semi-empirical LCAO SCF MO method with various degrees of approximations. The results have been analysed with regard to the following two factors: (a) The difference in effective electronegativity between the carbon atoms in the four-membered ring and the other carbon atoms in the molecule. (b) The inclusion of doubly excited configurations in the description of the π-electronic molecular states. The theory satisfactorily interprets the excitation energies and the nature of the electronic transitions. The predictions are particularly affected by the inclusion of the doubly excited configurations. On the basis of these results, the empirical parameters used are discussed.
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    International Journal of Quantum Chemistry 3 (1969), S. 73-78 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: An adiabetic theory of spin lattice relaxation is proposed. It is shown that if one takes account of the adiabatic adaptation of the electrons to the motion of the ionic complex the motor of the relaxation is not the crystalline potential modulation but the fluctuation of the effective magnetic field produced by the complex near the paramagnetic system.
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  • 29
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    International Journal of Quantum Chemistry 3 (1969), S. 107-113 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Using the natural orbital representation and optimizing the exponents in the Slater-type orbital basis, configuration interaction type wave functions for the helium atom are given which combine compactness and high accuracy.
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    International Journal of Quantum Chemistry 3 (1969), S. 141-143 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 31
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    International Journal of Quantum Chemistry 3 (1969), S. 185-194 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Polarization is shown to play a non-negligible role in two properties of the ground state of benzene-iodine type complexes: their dipole moment, and the halogen infrared spectrum. These results, compared with preceding results concerning π-π complexes, suggest that the ground-state properties of charge-transfer complexes should not be interpreted exclusively by the usual resonance mode.
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    International Journal of Quantum Chemistry 3 (1969), S. 225-230 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The zero-field splitting parameters D, E, and D* are calculated theoretically for four phenyl naphthalenes. Esr measurements show that the theoretical calculations are in good agreement with experiment. Comparison of the theoretical and experimental results gives some insight into the geometry of these molecules in their lowest triplet state.
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    Notes: The quantum theory of the Faraday effect or magnetic rotatory power is set up for diamagnetic molecules and is based upon a variation-perturbation method which, unlike the usual Dirac perturbation theory, needs only the knowledge of the wave function ψ0(0) of the ground state of the non-perturbed molecule. The principle of this theory includes in the expression of the perturbed wave function, vectors which characterize the contribution of the different fields of perturbation. The quantities which descríbe the Faraday effect, obtained from the calculation of the electric and magnetic macroscopic dipole moments, are expressed from ψ0(0) and the vectors precedently introduced. They are determined by a variation calculus.
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    International Journal of Quantum Chemistry 3 (1969), S. 503-511 
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    Topics: Chemistry and Pharmacology
    Notes: The ground state wave-function of a two electrons atom may be represented to any accuracy by a 1S projected Slater determinant built on hypercomplex spin-orbitals.
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    International Journal of Quantum Chemistry 3 (1969), S. 535-535 
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    International Journal of Quantum Chemistry 3 (1969), S. 553-568 
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    Notes: Single-exponential functions of the forms 1s̄ = 1s, 2s̄ = N1(2s + b1s + a3s), 2p̄ = N2(2p + c3p) are introduced as an alternative to the Slater orbitals 1s, 2s, 2p for the atoms of the first period. The orbitals are intended for molecular calculations and the parameters a and c should be chosen in order to make the basis consistent with a given preliminary description of the molecule: see Part I, G. Del Re, Intern. J. Quantum Chem. 1, 293 (1967), but, first of all, a study of their behavior in atomic systems is necessary. Therefore orbital exponents and total atomic energies are determined by optimization: the promotion coefficients a and c are zero for best-atoms and the functions become strictly hydrogen-like orbitals. Comparisons are allowed with Slater's, Roothaan's, Ransil's and SCF orbitals.Given promoted 2s̄ and 2p̄ orbitals on carbon atoms in a carbon-carbon sigma bond, we fix the coefficient a and c in order to obtain one center sp orbitals orthogonal to one another. These are discussed, mapped and compared with the two center hybrids obtained by the Löwdin orthogonalization.
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    Notes: Procedures are presented which are expected to produce good numerical lower bounds to eigenvalues for Hamiltonians having continuous spectra. Further, it is observed how these lower bounds can be utilized in other estimation methods.
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    Notes: A general formalism is presented for the determination of the optimum natural orbitals within the various strongly orthogonal geminals of a wavefunction describing a 2N-electron closed-shell molecule or atom. The relationship to Hartree-Fock-Roothaan theory is established; the algorithm that is developed is quadratically convergent to the desired result, and does not ignore off diagonal Lagrangian multipliers, or require an infinite series of 2 × 2 orthogonal transformations of the original basis.
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    International Journal of Quantum Chemistry 3 (1969), S. 711-722 
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    Notes: The generalized algebraic eigenvalue problem (A - λB)x = 0 arises in the use of the variation method in quantum mechanics. If, within the limitations of the computer word-length, the basis set used to expand the trial wave function is linearly dependent, the matrix B becomes singular. Three different algorithms designed to deal with this difficulty have been investigated, paying special attention to the problem of identifying which members of the basis set are effectively linearly dependent. The advantages and limitations of each method are discussed.
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    Notes: Using the Rayleigh-Schrödinger perturbation formalism, expressions are obtained for the nth order energy and the nth order wave function. No restrictions are placed on the degeneracy of the state or the order of perturbation in which the degeneracies are resolved. By the use of suitable operators, the formulae are expressed in compact form.
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    International Journal of Quantum Chemistry 3 (1969), S. 823-849 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The long range intermolecular forces in terms of the interaction energies between two conjugated molecules are computed and discussed for the cases: (a) a point charge and ethylene, (b) two ethylene molecules, (c) two hexatriene molecules, (d) two benzene molecules, (e) two naphthalene molecules, and (f) two polar merocyanine molecules. The calculations are based on Buckingham's theory of long range intermolecular forces and the author's values for multipole moments and polarizabilities presented previously. The advantage of the treatment is: asymmetric molecules are correctly described and the intermolecular potential is better approximated than by the usual dipole approximation.
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    International Journal of Quantum Chemistry 3 (1969) 
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    International Journal of Quantum Chemistry 3 (1969), S. 781-793 
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    Topics: Chemistry and Pharmacology
    Notes: Radiation damping of three atoms in a radiation field is studied for both a linear and closed-chain configuration. One atom of the system is initially excited. Use is made of the Heitler-Ma perturbation procedure up to second order. The discussion is developed in terms of the symmetry of the interactions within the system. The interactions arising from dipole transitions perpendicular to the plane of the closed chain are shown to be similar to the interactions in a two-atom system, and the results are extended to cover larger rings.
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    International Journal of Quantum Chemistry 3 (1969), S. 1064-1066 
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    International Journal of Quantum Chemistry 3 (1969), S. 1-2 
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    International Journal of Quantum Chemistry 3 (1969), S. 45-56 
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    Topics: Chemistry and Pharmacology
    Notes: The configuration interaction method has been applied to the H2 and H3 systems. The effect of increasing the size of the atomic Slater-type orbital basis has been studied. A minimization procedure with respect to orbital exponents has been carried out.
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    International Journal of Quantum Chemistry 3 (1969), S. 93-105 
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    Notes: The rotational projection operator previously introduced [12] serves here to build up an explicit formula for the non-relativistic energy associated with a spin-projected determinant. Corresponding orbitals are used throughout, and interchange of configuration space and Euler angles integrations provides rapidly an energy expression previously obtained either by use of Löwdin's projector (via first- and second-order density matrices (8)) or by mixed space and spin permutation operator (GF method (9)).
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    International Journal of Quantum Chemistry 3 (1969), S. 893-901 
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    Topics: Chemistry and Pharmacology
    Notes: The protonic conductivity in ice crystals is considered within the framework of strong coupling developed earlier by the present authors for semiconductors with narrow bands and strong coupling of electrons with phonons. The generalization for a two-band model is developed. The model used is the one described by Gosar and Pintar, the principal feature of which is the concept of the protonic conduction bands. The analytical expression for the protonic mobility is given. The results of the theory are in qualitative agreement with the experimental data.
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    International Journal of Quantum Chemistry 3 (1969), S. 931-943 
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    Topics: Chemistry and Pharmacology
    Notes: An extended method of calculation for two shells of atomic electrons, based upon the use of non-orthogonal radial orbitals, is presented. The rules for going over from the radial integrals of the ordinary method of calculation to the linear combinations of radial integrals of the extended method of calculation are given. The numerical calculations are carried out for the ground states of lithium- and beryllium-like atomic systems.
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    International Journal of Quantum Chemistry 3 (1969), S. 1013-1025 
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    Topics: Chemistry and Pharmacology
    Notes: All-electron SCF-LCAO-MO computations for diazomethane, ketene and allene are presented. The basis functions are contracted Gaussian orbitals. Theoretical results are discussed and related to available experimental data.
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    International Journal of Quantum Chemistry 3 (1969), S. 1055-1058 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 1067-1068 
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    International Journal of Quantum Chemistry 3 (1969) 
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    Notes: A method for the determination of the virtual orbitals for configuration interaction is described. This method is a generalization of the one used by Watson in 1960 for the ground state of the beryllium atom. The important point in the method is to complete the set of functions used successively. As an illustration the method is applied to the ground state of the beryllium atom. The method seems to be efficient.
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    International Journal of Quantum Chemistry 3 (1969), S. 57-66 
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    Notes: Variational upper and lower bounds for the overlap between an approximate and the true wave function are proposed, and it is shown that the error bounds introduced recently by Gordon are special cases of the variational formulas.
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    International Journal of Quantum Chemistry 3 (1969), S. 79-92 
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    Notes: The π-electron distributions, spin densities, and energies of the first triplets of the nucleotide bases, uracil, thymine, cytosine, adenine, and guanine, were investigated in various semiempirical approximations. Results are presented for calculations using the semiempirical form of the closed-shell SCF configuration interaction method, of the different orbitals for different spins (unrestricted Hartree-Fock) treatment, with and without spin projection, and of the Roothaan's open-shell procedure.
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    International Journal of Quantum Chemistry 3 (1969), S. 635-650 
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    Notes: Iterative methods for the calculation of the lowest eigenvalue and the corresponding eigenvector are derived from the partitioned Schrödinger equation in matrix form. While they have a formal similarity to the Brillouin-Wigner perturbation expansion, they converge for a much wider class of matrices. The double iteration methods (DIM and DIMA) lead to a series of upper and lower bounds to the desired lowest eigenvalue in accordance with Löwdin's bracketing theorem and can be used in a strategy which insures convergence to the solution for arbitrarily large perturbations. A much more efficient single iteration method (SIMA) produces the proper solution even for numerically very ill-conditioned matrices (large offdiagonal elements and small separation of the diagonal elements from the lowest). An important feature of the iterative methods is their insensitivity toward roundoff errors which makes them especially suited for very large matrices, where direct diagonalisation, for example by the Jacobi method, is impracticable.
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    International Journal of Quantum Chemistry 3 (1969), S. 699-710 
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    Topics: Chemistry and Pharmacology
    Notes: A generalization of a theorem on off-diagonal hypervirial relations is obtained and is used to demonstrate when to expect exact solutions of eigenvalue problems using the hypervirial method. Links are established between the hypervirial method and other approximation methods. The harmonic oscillator and hydrogen atom problems are given as examples.
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    International Journal of Quantum Chemistry 3 (1969), S. 750-750 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 1001-1012 
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    Topics: Chemistry and Pharmacology
    Notes: The mirror reflection symmetry which consists in the correlation of the substitution j → -j -1 with the reflection of the coordinate system and of m → -m with the reflection of the space with respect to the xy-plane has been applied to the quasi-spin formalism. The phases of the wave functions of the shell of equivalent atomic electrons treated as partially filled, as they relate to those when the same shell is treated as almost filled, have been established. The mirror reflection symmetry has been generalized for the supplementary quantum numbers used for distinguishing the terms of the same kind. The phases of the coefficients of fractional parentage of almost filled shell enabling us to determine them from those of partially filled shell have been specified. Corresponding phase relations for the matrix elements of operators have also been considered.
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    International Journal of Quantum Chemistry 3 (1969), S. 1058-1061 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 749-749 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 751-751 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 64
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    International Journal of Quantum Chemistry 3 (1969), S. 767-780 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The explicit form of a projection operator constructed from a linearly dependent set is found. The relationships with canonical orthonormalization and with the cofactor matrix of the set's metric matrix are discussed. Similar expressions are obtained for the inner projection of a positive definite operator using a linearly dependent set.
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    International Journal of Quantum Chemistry 3 (1969), S. 269-287 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 327-347 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: This paper examines the relationship between the topographical features of a molecular charge distribution and the kinetic energy of the system. Specifically, the spatial contributions to the kinetic energy are related to the Laplacian of the total charge density and to the gradients of the natural-orbital densities. It is concluded that a necessary requirement for molecular stability is the existence of a net negative curvature for the molecular charge distribution in the internuclear region. It is shown that the charge density accumulated in the internuclear region of a stable molecule is distributed in such a way as to keep the accompanying increase in the kinetic energy to a minimum. A comparison of the contributions to the kinetic energy from the atomic and molecular charge distributions indicates that in the formation of a stable molecule the contribution from the molecular charge density in the binding region is decreased relative to that of the atoms.
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    International Journal of Quantum Chemistry 3 (1969), S. 489-492 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: A method for the evaluation of the Fourier transform of two-center functions is presented.
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    International Journal of Quantum Chemistry 3 (1969), S. 513-521 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: A translation is made of spin projection methods into the language of second quantization. This leads to a new formula for the Sanibel coefficients and expressions convenient to use for automatic calculation of spin projections.
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    International Journal of Quantum Chemistry 3 (1969), S. 537-551 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The problem of evaluating the long range terms (electrostatic, polarization, dispersion) of the interaction energy between molecules at intermediate distances (i.e. distances of the order of magnitude of the molecular dimensions) is considered. Instead of being approximated by its dipole part, the exact interaction Hamiltonian is treated as proposed by Longuet-Higgins [11], i.e. the matrix elements are interpreted as electrostatic interactions between state and transition charge distributions. These charge distributions are approximated in a systematic way by sets of point charges (localized on the atoms) or sets of dipoles (localized on the bonds). The various contributions to the energy may then be expressed in terms of atomic net charges and bond polarizabilities. More refined approximations of the charge distributions could be used and correspondingly improved formulae could be derived: as an example, a formula for the σ-π dispersion energy is derived, where the σ charge distributions are approximated by bond transition dipoles (leading to σ bond polarizabilities in the final formula) while the π charge distributions are approximated by atomic charges.
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    International Journal of Quantum Chemistry 3 (1969), S. 1061-1064 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 881-887 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The ethylene molecule has been investigated by means of the General SCF-MO-LC(LCGO) Program System for 12 different nuclear positions, taking all electrons into account. The equilibrium distances and angles as well as all force constants of the totally symmetric vibrations with the corresponding frequencies have also been calculated.
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    International Journal of Quantum Chemistry 3 (1969), S. 983-999 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Semi-empirical calculations of the π-band structure of planar and three-dimensional graphite are described. Special attention is given to the significance of band parameters. The theoretical results are in good agreement with experiment.
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    Notes: Expressions of the matrix elements of the spin-other-orbit and spin-orbit interactions for the various multiplets of all the states of ƒ2- and ƒ3-electron configurations are reported and used to evaluate the Hartree-Fock values of these interactions in the neutral atoms Ce(4ƒ2), Pr(4ƒ3), Ho(4ƒ11) and Er(4ƒ12). The required values of the spin-spin parameters M(K)s, and the spin-orbit parameter ζ for these atoms were obtained using numerical Hartree-Fock wave functions.
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    International Journal of Quantum Chemistry 3 (1969), S. 1069-1070 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 17-24 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 25-32 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The method of calculating wave functions for an electron-nucleon system by a variational method originally suggested by Born and Oppenheimer [1] is rigorously investigated. As an application we sketch the calculation of a simple nonadiabatic wave function for the system.
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    International Journal of Quantum Chemistry 3 (1969), S. 246-246 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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  • 78
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    Notes: Methyl groups in flavins are best treated by the group-orbital approximation. The pseudo-heteroatom approximation overestimates methyl hyperconjugation with the Pariser-Parr-Pople SCF-MO method. Singlet π → π* transition energies are calculated by various MO methods with differing degrees of sophistication, and the results from the P—P—P method agree reasonably with the experimental values. 2- and 4-thioflavin analogs are also treated satisfactorily. The effects of position and number of the methyl groups on the spectra of flavins are described in detail. Rough estimates of the n → π* energies of flavins suggest that the lowest singlet excited state is (π, π*), consistent with the fluorescence and phosphorescence polarization data.
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    International Journal of Quantum Chemistry 3 (1969), S. 349-370 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The convergence radius of the series expansion for the energy of H2+ in the δ-function model (in terms of the perturbation parameter μ/λ, where μ is the charge of the perturbing nucleus and λ the fixed charge of the other nucleus) is investigated. A lower bound of this convergence radius (possibly equal to it) previously defined by Robinson [5] is studied analytically as a function of the internuclear distance R and computed numerically. The results differ strikingly from those previously obtained by Robinson who used a simplified but poorer lower bound: in contrast with this poorer bound, the one studied in the present paper is larger than for I every R, from which fact it may be concluded that, contrary to Robinson's previous result, the series expansion of the energy, in the δ-function model under consideration, still converges when μ = λ for every R.
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    International Journal of Quantum Chemistry 3 (1969), S. 123-130 
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    Topics: Chemistry and Pharmacology
    Notes: The first part of this paper gives an introduction of different kinds of atomic associations. Furthermore it will be shown that partial systems of united atoms are not only described by their nuclear-charge number, but additionally by their number of electrons. Both characteristics of a partial system of atomic associations may lead to an apparent multiple-valuedness in the transitions between atomic associations. It is shown that the multiple-valuedness of the atomic associations can be understood and eliminated within the Born-Oppenheimer-approximation, which leads to the concept “energyhypersurface”. An example is given by the system {He, H, H, H}+.
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    International Journal of Quantum Chemistry 3 (1969) 
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    International Journal of Quantum Chemistry 3 (1969), S. 195-204 
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    Topics: Chemistry and Pharmacology
    Notes: In this paper a variational principle proposed by Hall [1] is shown to be a minimum principle for coulombic systems. Into this principle it is possible to admit a larger class of trial wave functions than is possible in the conventional variational treatment, including wave functions with discontinuities. It is further shown that the upper bounds given by this treatment are always at least as good as that given by the Rayleigh-Ritz method.The theory is then applied to the hydrogen atom and upper bounds to the energy are calculated for various “cutoff” wave functions. It is usually possible to define an optimum “cut off” distance which minimizes the upper bound.
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    Notes: Polarization tensors are discussed in terms of their intrinsic symmetry group which is a direct product of the point group and the subgroup of the permutation group relevant to the experiment. The study of these latter groups is simplified by use of the isomorphism with certain point groups and permutations of suffixes can be visualized by rotations and reflections of the vertices of various objects in space. The approach unites the previous treatments and provides a means of constructing the bases for the irreducible tensor components. The difficulties introduced by Laplace's equation are explained and the information obtainable from induced birefringence experiments (Kerr and Cotton-Mouton effects) discussed for various systems.
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    International Journal of Quantum Chemistry 3 (1969), S. 247-247 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Notes: Several classes of functions related to the Gaussian have been used with success as basis sets for the representation of atomic and molecular orbitals.We have compared the representation of a hydrogen 1s orbital by a sum of Gaussian lobe functions with its expansion in eigenfunctions of the three-dimensional isotropic harmonic oscillator. The lobe functions are shown to achieve better expectation values of the energy, with fewer terms. The lobe functions have the further computational advantage of not containing high powers of the radius.It is concluded that the lobe functions are a superior basis set for use in calculations of the electronic structure of atoms and molecules.
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    International Journal of Quantum Chemistry 3 (1969), S. 373-376 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 371-373 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: It is shown that the familiar Temple, Stevenson-Crawford, and Weinstein lower bound formulas for eigenvalues are consequences of a much stronger general lower bound formula and the weak “Eckart criterion” for the overlap of the approximate and true wave functions.
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    International Journal of Quantum Chemistry 3 (1969), S. 397-415 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Two-center one-electron integrals needed in certain molecular correlated wave function calculations, using one-center expansion approximation, have been studied. The form of the basic correlated function used in this study is \documentclass{article}\pagestyle{empty}\begin{document}$$ h(r_{12}) = r_{12}^n e^{ - \zeta r_{12} } $$\end{document} The parent integral is expressed in terms of an angular integral, and an auxiliary radial integral depending upon the variables r1, r2, and r12. Several analytical formulas, and a recursive formula are derived for the auxiliary integral, and other related integrals. All these formulas are given in computationally useful forms. Logical flow charts and FORTRAN programs were constructed for computing the basic integrals discussed in the paper. Numerical values of some integrals, thus obtained, are tabulated for comparisons.
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    Notes: We have studied the validity of the traditional model of a dimer that has been treated exactly by Merrifield and Fulton and Gouterman, solving the vibronic coupled equations by a numerical method. This model takes into account the modification of the nuclear equilibrium configuration, but it neglects the variation of the force constant when the monomer is electronically excited from the fundamental to a given excited state (the corresponding electronic potentials are both considered as harmonic). We have shown by inspection of the absorption and fluorescence spectra calculated by solving the vibronic equation exactly that the variation force constant cannot be neglected, even if it is weak, particularly in the weak coupling region. The weak, intermediate and strong coupling criteria have been deduced, for the model studied, by examination of the dimeric electronic potential surfaces for different cases of intermolecular interactions.
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    International Journal of Quantum Chemistry 3 (1969), S. 485-487 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: It is emphasized that for the theoretical consideration of many problems of defect centers in crystals (especially of problems which need the correct asymptotic behavior of the wave functions) the semiempirical approach can be effective. As an example the spontaneous radiative time decay of the excited F-center in alkali halides is calculated by using the experimental energies of absorption and emission bands.
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    Topics: Chemistry and Pharmacology
    Notes: Pauling's formulas for the calculation of matrix elements for valence bond functions are derived using a simple substitutional process. The results generalize and simplify the formulas. In particular, the formulas do not depend upon orthogonality of atomic orbitals nor upon the nature of the choice of bond structures (canonical or not). The results are particularly adaptable to automatic computation.
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    International Journal of Quantum Chemistry 3 (1969), S. 593-610 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The general formalism of the variational theory of the Faraday effect established in the first part of this paper is now applied to the actual computation of the Verdet constant of the hydrogen molecule, of water and of some saturated hydrocarbons. The numerical results have a correct order of magnitude and even, for hydrogen, are rather close to the experimental value.
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    International Journal of Quantum Chemistry 3 (1969), S. 493-501 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: Expansions in terms of the spherical coordinates of two particles are given for the interparticle distance and its inverse. The expansions are characterized in that each term is a product of analytical one-variable functions. While it is possible to find acceptable expansions for r12, those obtained for r12-1 exhibit extremely slow convergence, unacceptable for practical use. The same objections must be raised against related expansions of multi-centered molecular integrals.
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    International Journal of Quantum Chemistry 3 (1969) 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Notes: This article gives pointwise bounds for the wave functions of one-electron molecular systems.
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    International Journal of Quantum Chemistry 3 (1969), S. 115-121 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
    Notes: The wave function of the HeHHe+ molecule has been calculated by means of the GENERAL SCF-MO-LC(LCGO) PROGRAM SYSTEM, taking all four electrons into account. The calculations were carried out for a number of linear equidistant, linear non-equidistant, and bent nuclear arrangements. The minimum energy of -5.7930 a.u. was found for a linear equidistant configuration with a He—H distance of 0.939 Å. The corresponding ionization energy was 37.9 eV. An estimation of the energy of formation of HeHHe+ from HeH+ and He based on SCF-calculations on HeH+ and He gave 7.9 kcal/mole. The frequencies of the normal vibrations were calculated.
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    International Journal of Quantum Chemistry 3 (1969), S. 145-145 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    International Journal of Quantum Chemistry 3 (1969), S. 169-184 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We discuss the properties of one version of the least squares (LS) method for the solution of the Schrödinger equation. These properties are exemplified by a number of calculations on the n1S and n3S states of helium, up to principal quantum number three, which are very much more accurate than previous LS calculations on helium. Particular attention is paid to the convergence properties of the LS procedure and we compare it with the simpler Rayleigh-Ritz (RR) procedure in the case when the RR matrix elements are evaluated numerically over the same quadrature mesh as used in the LS procedure. We conclude that although the LS procedure is capable of high accuracy it has no advantages which would justify its sole use in place of the RR procedure. However, it does have some advantages when used in conjunction with RR, in that it gives an estimate of the numerical accuracy of the RR energies.
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    International Journal of Quantum Chemistry 3 (1969), S. 205-218 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The biorbital theory called also “identical geminals theory” is applied to the study of a number of conjugated molecules. All basic integrals are determined by means of the Pariser-Parr-Pople procedure. The biorbital theory reproduces about 40 per cent of the correlation energy of the ground state of the molecule; this number is raised to about 70 per cent for the lowest triplet state. The low lying excited states are well represented from the point of view of transition energy as well as from the point of view of symmetry. The occupation number matrix and the charge-bond order matrix are defined and discussed. The overall chemical description of conjugated molecules produced by the biorbital theory is similar to that produced by other theories of electronic structure of molecules. It is concluded that the biorbital theory provides a description the quality of which is, roughly speaking, about half way between those provided by the SCF-MO and complete CI theories, respectively.
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    International Journal of Quantum Chemistry 3 (1969), S. 246-247 
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    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
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    Topics: Chemistry and Pharmacology
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